The covering numbers and ``low M^-estimate" for quasi-convex bodies

The covering numbers and ``low M^-estimate" for quasi-convex bodies

This article gives estimates on the covering numbers and diameters of random proportional sections and projections of quasi-convex bodies in \myR. These results were known for the convex case and played an essential role in the development of the theory. Because duality relations cannot be applied i...

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Veröffentlicht in:Proceedings of the American Mathematical Society 1999-05, Vol.127 (5), p.1499-1507
Hauptverfasser: Litvak, A. E., Milman, V. D., Pajor, A.
Format: Artikel
Sprache:eng
Schlagworte:
Banach space
Convexity
Ellipsoids
Functional analysis
Mathematical constants
Mathematical inequalities
Mathematical theorems
Numbers
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Zusammenfassung:This article gives estimates on the covering numbers and diameters of random proportional sections and projections of quasi-convex bodies in \myR. These results were known for the convex case and played an essential role in the development of the theory. Because duality relations cannot be applied in the quasi-convex setting, new ingredients were introduced that give new understanding for the convex case as well.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-99-04593-1